(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let T1 be the reflection about the line 2x–5y=0 and T2 be the reflection about the line –4x+3y=0 in the euclidean plane.

(i) The standard matrix of T1 o T2 is: ?

Thus T1 o T2 is a counterclockwise rotation about the origin by an angle of _ radians?

(ii) The standard matrix of T2 o T1 is: ?

Thus T2 o T1 is a counterclockwise rotation about the origin by an angle of _ radians?

2. Relevant equations

I think these equations are correct...

T(v) = A(v)

Reflection:

A =

[((2(u_1))^2)), (2(u_1)(u_2)))

(2(u_1)(u_2)), ((2(u_2))^2))]

*u being the unit vectors

Rotation counterclockwise:

A =

[cosx -sinx

sinx cosx]

S o T is the matrix Transformation with matrix AB

3. The attempt at a solution

I thought I understood this, but again, I guess I've understood something incorrectly.

For the first question, I got the unit vectors to be:

[(5/sqrt29)], (2/sqrt29)] and [(3/5), (4/5)] for T_1 and T_2 respectively.

I then got the standard matrix A of T_1 to be:

[(21/29) (20/29)

(20/29) (-21/29)]

and the standard matrix B of T_2 to be:

[(-7/25) (24/25)

(24/25) (7/25)]

I then took AB = the dot product of these matrices to get:

[(333/6350) (644/6350)

(-644/6350) (333/6350)]

I did similar for the second part, but I'll spare all the numbers, since I'm messing something up....

Further, how would I go about getting the radians? I know the formula for counterclockwise rotation, but wouldn't know how to come up with the radians of such a number...

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Composite Matrix Transformation - Reflection

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